For the reduction of structural noise and vibrations, passive techniques are widely used, and active control has now been widely studied. At the meeting of both approaches, semi-passive techniques have seemed to be too limited, until recently and a new technique: Synchronized Switch Damping on Inductance (SSDI). For the modelization of this method in a piezo-structural context, we wrote a new formulation based on the electrical displacement. Its use in a finite-element code allowed us to simulate simple cases on beams in low frequency. This was validated with experiments. For structural acoustics cases, we designed a specific test setup in order to study the interaction of structural vibrations with the sound in enclosures: a box composed of five rigid walls, the sixth wall being flexible and excited by a shaker. The experiments showed that substantial reduction of vibrations can be achieved in low frequency at various peaks when using various piezoelectric patches on the plate, connected to the SSDI devices. In some cases, good reduction can also be obtained on the noise level. Comparison with active control was less favourable, but interesting possibilities could emerge by mixing the two techniques at the same time.